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laboutique.edpsciences.fr-000681 03 01 01 000681 03 9782759807048 15 9782759807048 00 BA 02 1 mm 01 1 mm 08 1 gr 10 01 02 Universitext Co-édition SPRINGER-EDP Sciences sur les maths (titres de la Collection Savoirs Actuels). 01 01 Morse Theory and Floer Homology 1 A01 01 A945 Michèle Audinet Audinet, Michèle Michèle Audinet 2 A01 01 A560 Damian Mihai Mihai, Damian Damian Mihai Damian Mihai, maître de conférences à l'Université de Strasbourg, est spécialiste de géométrie et topologie symplectiques. (au moment de la parution de l'ouvrage) 1 01 eng 00 596 03 24 Izibook:Subject Mathématiques 24 Izibook:SubjectAndCategoryAndTags |Mathématiques| 10 2011 MAT000000 29 3052 01 510 05 05 00 This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the number of 1-periodic trajectories of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold. The first part is a thorough introduction to Morse theory, a fundamental tool of differential topology. It defines the Morse complex and the Morse homology, and develops some of their applications. Morse homology also serves as a simple model for Floer homology, which is covered in the second part. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been crucial in the recent achievements in symplectic geometry and in particular in the proof of the Arnold conjecture. The building blocks of Floer homology are more intricate and imply the use of more sophisticated analytical methods, all of which are explained in this second part. The three appendices present a few prerequisites in differential geometry, algebraic topology and analysis. The book originated in a graduate course given at Strasbourg University, and contains a large range of figures and exercises. Morse Theory and Floer Homology will be particularly helpful for graduate and postgraduate students. 03 00 This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the number of 1-periodic trajectories of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of the underlying manifold. The first part is a thorough introduction to Morse theory, a fundamental tool of differential topology. It defines the Morse complex and the Morse homology, and develops some of their applications. Morse homology also serves as a simple model for Floer homology, which is covered in the second part. Floer homology is an infinite-dimensional analogue of Morse homology. Its involvement has been crucial in the recent achievements in symplectic geometry and in particular in the proof of the Arnold conjecture. The building blocks of Floer homology are more intricate and imply the use of more sophisticated analytical methods, all of which are explained in this second part. The three appendices present a few prerequisites in differential geometry, algebraic topology and analysis. The book originated in a graduate course given at Strasbourg University, and contains a large range of figures and exercises. Morse Theory and Floer Homology will be particularly helpful for graduate and postgraduate students. 02 00 This book is an introduction to modern methods of symplectic topology. It is devoted to explaining the solution of an important problem originating from classical mechanics: the 'Arnold conjecture', which asserts that the number of 1-periodic trajectories of a non-degenerate Hamiltonian system is bounded below by the dimension of the homology of... 21 00 06 01 https://laboutique.edpsciences.fr/produit/681/9782759807048/morse-theory-and-floer-homology 01 00 03 02 https://laboutique.edpsciences.fr/system/product_pictures/data/009/981/724/original/L07048_couvweb.jpg 17 14 20240913T172338+0200 01 P1 EDP Sciences 01 01 P1 EDP Sciences 17 avenue du Hoggar - PA de Courtaboeuf - 91944 Les Ulis cedex A http://publications.edpsciences.org/ 04 01 00 20140201 19 00 20140201 2026 06 3052868830012 01 WORLD WORLD 08 EDP Sciences 04 01 00 20140201 03 01 D1 EDP Sciences 21 04 05 01 02 1 00 73.84 01 5.50 3.85 EUR